In Figure REF , we compare the distribution of \(j\)  versus \(V_{\rm flat}\)  for galaxies described in this
section with the distributions of \(j_{200}\) , \(j_{2000}\) , and \(j_{20,000}\)  versus \(V_{200}\)  for
dark matter haloes from Figure REF . As discussed above, it is assumed that haloes have
the same rotation velocities as the galaxies they host, so they can be directly compared in
Figure REF . The halo relations from Figure REF  for \(V_{20,000}\)  are not shown because they
are not significantly different from those for \(V_{200}\) .
We fit a linear relation to the galaxies using 100
bootstrap re-samplings and a generalised least squares fitting routine [1]}, which gives a slope
of \(2.5\pm 0.1\)  rms. We also fit a linear relation to the haloes in Figure REF 
for \(j_{200}\)  versus \(V_{200}\)  for circular velocities which span the velocity range of the galaxies, \(125 < V_{200} < 315\)  km s\(^{-1}\) .
This results in a slope of \(1.92 \pm 0.02\)  rms. The distribution of galaxies
has a similar slope to that of the haloes, as found by [2]} and others [3]}, [4]},
and approximately half the average rms scatter (0.15 dex versus 0.27 dex). The lower scatter compared to the haloes
is related to the finding by [5]} that the width of the observed scale-radius distribution of galactic discs
is narrower than that expected from the distributions of halo spin parameters in cosmological simulations.
For the halo \(j_{2000}\) 
versus \(V_{200}\)  and \(j_{20,000}\)  versus \(V_{200}\)  relations, the slopes are \(1.80 \pm 0.02\)  and \(1.26 \pm 0.02\) , respectively,
and the average rms scatters are 0.28 and 0.26, respectively.
The slopes flatten slightly with increasing \(\Delta \) , but the scatter remains constant to within errors.
Given all the factors not included in our simple picture, we consider it remarkable how similar the galaxy
and halo slopes are. The main result of this paper is encapsulated in the much larger difference in normalisation between
galaxies and haloes. We choose to measure this difference at approximately the center of the distributions, at log \(V_{rot}\) =2.35 (\(V_{rot}= 224\)  km s\(^{-1}\) ).
The average normalisation of the galaxies is less than that of the haloes
for \(j_{200}\)  by a factor of \(\sim 2\)  (0.30 dex), consistent with previous studies [4]}, [7]}.
The average normalisation of the galaxies is greater than that of the haloes for
\(j_{2000}\)  and \(j_{20,000}\)  by factors of \(\sim 2\)  (0.30 dex) and \(\sim 5.6\)  (0.75 dex), respectively.
